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Let's assume we have an air-spaced inductor made of copper wire.

As temperature changes, due to thermal expansion of physical dimensions of the coil, its inductance changes too.

1) Is there a way to control the thermal coefficient of inductance somehow (like using some clever coil shape or something)? I would love to be able to tune the temperature coefficient in the range $\pm 30\:\rm{ppm/C}$.

2) Is there a way at least to make the temperature coefficient significantly lower than the coefficient of thermal expansion of copper ($<10\:\rm{ppm/C}$)?

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I am not sure whether you can optimize the shape to reduce the influence of thermal expansion. What often helps for high precision instruments is a precise temperature control. You heat up the important bits to a value above room temperature and try to keep it exactly at, for example, 35°C. With only tiny temperature variations remaining, the influence on the dimensions is also reduced by orders of magnitude compared to a normal instrument where the inductor is operating in a wide temperature range (18-30°C, depending on room temperature). – Alexander Mar 20 '12 at 16:34
The active temperature control that @Alexander suggests is a common strategy...even for vacuum filled instruments like the precision beam current monitors used at JLAB because changes in the size of the instrument affect their gain. – dmckee Mar 20 '12 at 16:58
I am already in oven-controlled environment. My goal here is to match temperature coefficient of inductor to ones of other pieces of the circuit to lower temperature impact even further. – BarsMonster Mar 21 '12 at 3:01
up vote 1 down vote accepted

Obviously if the coil linearly expands equally and uniformly in all three dimensions, the inductance has to scale in directly proportionality to the dimension. My understanding is that anything made of pure copper, no matter what you do with it, will expand equally and uniformly in all three dimensions.

If you can incorporate materials with different thermal expansion coefficients than copper, you could maybe constrain or push the coil in one of the dimensions, changing its shape a bit as the temperature changes.

If that doesn't work, it seems to me that your only choice is to use a core which is not air (or at least, not entirely air). You could look for something with temperature-dependent $\mu$, to take an obvious example. Or something where $\mu \neq 1$ but that expands in a different way than the copper. I'm not sure what your constraints are for the core.

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Frequencies are in 10-100Mhz range, so not many materials could be placed there... – BarsMonster Mar 23 '12 at 11:54

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